I want to create pictures, with the movement of the sun. I've tried doing it as HDR photos, but you cant really see the sun. I just get pictures with nothing really. When it's at the horizon, I get that star-look, but nothing else, not the effect I was hoping for.
I've tried editing a bit, but it doesn't help at all

Definitely don't use HDR blending techniques. You just want to do a simple image stack - most more advanced editing systems (Photoship, Paint Shop Pro, etc) can do layering, pretty much unlimited numbers limited only by the memory of your computer. The blending mode should be switched to 'lighten'. If you set the camersa to manual, fix its position and location on a firm tripod, you can fire off shots as the sun moves through the frame - the main thing will be making sure all of the exposures are identical. This way, the only difference in each frame will be the location of the sun itself. BY using 'lighten' as the blend mode, the sun will be always be lighter than the sky, so each frame where the sun has moved position the blend will show through only the sun. The rest of the exposure should remain exactly as you shot it and remain only 1 frame. Now if you WANT an HDR effect on the surrounding landscape, you could do one additional exposure for the foreground, and do an HDR blend of that landscape with your merged sky/sun shot.

Well I don't care much for the "HDR effect" in this particular picture.

Layers, does it mean I have to buy photoshop. I have Lightroom and the HDR is made by a free plugin I downloaded.
Is there a similar plugin for stacking?

Lightroom is fine for me, the stuff PS does, I don't really use. There are only af few things PS can do, that LR doesn't have - its HDR, stitching panoramas, and now apprently stacking. And thats just extra features PS has.

HDR I got in Enfuse
Panoramas I have Hugin, even though I haven't tried it out yet.

This is what I get in GIMP.
The colors are horrible, but I can adjust that, the big problem is that there is only "one sun" the others are gone, but the sunbeam are still there. Not the Look I was going for.

The point of layers is to selectively mask and change opacity of each layer. If you simply stack them w/o any further manipulation of the masks then you will only achieve a triple exposure. The point of GIMP is that it allows you to modify the blending of different images to your final taste.

Since you stated you wanted control over layers but now are unsatisfied w/ having layer control, I am unclear what direction you actually want to take the photo in from a manipulation/editing stand point.

By the way, the major difference between your most recent post and the original is that the most recent one is a lot lighter, Can you post thumbnails or something to show us the source files so we can actually understand what the original images look like and also like a cartoon or word description of what you want the final image to look like.

The exposure definitely looks much nicer. As mentioned above, now that you've started stacking layers in GIMP, the next step is to change the mode that those layers are blended together. You are probably in the basic stacking mode, where there is no transparency at all. You have two primary controls with layers - blending mode and opacity. Most of these programs have a blending mode called 'lighten' whereby only the highlights or lightened sections of the photo will show through...the sun being clearly the brightest thing in your exposures will definitely show through on each layer if you choose this blending mode. The other option is to simply erase away the section of the layer where the sun is sitting behind on the previous layer...x2 for 3 layers. A little fine tuning and healing will make sure it doesn't look jagged or cut & pasted.

When using the lighten blend mode, it's fairly easy as long as your exposures are all matched between the 3 or 4 frames...only the sections of the photo that are lighter will show through - all other sections are untouched. For example, in this eclipse sequence of the moon, the camera was in a fixed location and fired 5 frames...the moon moved in each frame to a new location. When layering the 5 shots together - it required no editing at all - just set the blend mode of each layer to 'lighten' and that was it - the moon showed through in each new location in each frame, and the result is 1 shot with 5 moons:

You will need play with blending and masking to achieve a result similar to this. This is not something you can just drag and drop and expect instant final results. You will need to play around w/ your sources files to get a pleasing result, as zackiedawg has eluded to.